Question

Four point charges have the same magnitude of 2.0 × 10^-12 C and are fixed to the corners of a square that is 2.8 cm on a side. Three of the charges are positive and one is negative. Determine the magnitude of the net electric field that exists at the center of the square.

Answer 1

The formula is field E = k*q / d²
The trick for this problem is to recognize that, at the center of the square, the two +ve charges across from each other cancel out. You only need to consider the negative charge (field flows toward) and the charge across from it (field flows away).
The distance from the center to a corner is
d = 0.028m / √2 = 0.0197 m, so the field at the center due to the negative charge is
E = 8.99e9 N·m²/C² * 2.0 e-12C / (0.0197m)² = 46.32 N/C
toward the charge.
For the positive charge across from it, the magnitude of the field must be the same, but it too flows toward the negative charge.
Therefore the net field at the center is
E = 92.64 N/C toward the negative charge.